ILLUSTRATING QUADRATIC EQUATIONS || GRADE 9 MATHEMATICS Q1

Summary

This educational video script introduces the concept of quadratic equations, focusing on how to identify and arrange them into standard form, ax^2 + bx + c = 0. It explains the significance of coefficients a, b, and c, and provides examples to illustrate the process. The script emphasizes the importance of a being non-zero and the equation retaining its quadratic nature even if b or c equals zero. It concludes with an encouragement to like, subscribe, and stay tuned for more informative content.

Takeaways

• 📚 The video is about teaching how to identify the coefficients a, b, and c in a quadratic equation.
• 🔍 It emphasizes that a quadratic equation is in the standard form ax^2 + bx + c = 0, where a, b, and c are real numbers and a ≠ 0.
• 📐 The terms of the quadratic equation are defined: ax^2 is the quadratic term, bx is the linear term, and c is the constant term.
• 📉 The video provides examples of how to rearrange equations into the standard form and identify a, b, and c values.
• 🔢 It explains that if 'a' is 0, the equation becomes linear, not quadratic.
• 🚫 The importance of 'a' being a positive real number is highlighted to maintain the equation as quadratic.
• 📝 Examples given include equations like x^2 - 5x + 3 = 0, where a=1, b=-5, and c=3.
• 🔄 The process of converting equations into standard form by moving terms and changing signs to fit ax^2 + bx + c = 0 is demonstrated.
• 📌 The video clarifies that even if b or c equals 0, the equation can still be quadratic as long as a ≠ 0.
• 📘 It also covers how to handle equations with no linear term (b value) or no constant term (c value).
• 👍 The video concludes by encouraging viewers to like, subscribe, and hit the bell for more content.

Q & A

What is a quadratic equation?

A quadratic equation is a polynomial equation of the second degree, typically written in the form ax^2 + bx + c = 0, where a, b, and c are constants, and a ≠ 0.

What are the three terms in a quadratic equation?

The three terms in a quadratic equation are the quadratic term (ax^2), the linear term (bx), and the constant term (c).

What is the standard form of a quadratic equation?

The standard form of a quadratic equation is ax^2 + bx + c = 0, where a, b, and c are real numbers and a is not equal to zero.

How do you identify the values of a, b, and c in a given quadratic equation?

To identify the values of a, b, and c, first write the equation in standard form. The coefficient of x^2 is a, the coefficient of x is b, and the constant term is c.

What happens if the coefficient 'a' in a quadratic equation is zero?

If the coefficient 'a' is zero, the equation is no longer quadratic but becomes a linear equation.

What is the significance of the coefficient 'a' being positive in the standard form of a quadratic equation?

The coefficient 'a' being positive in the standard form ensures that the quadratic term is correctly represented and that the equation is in its proper form.

How do you rewrite the equation x^2 - 5x + 3 = 0 in standard form?

The equation x^2 - 5x + 3 = 0 is already in standard form, with a = 1, b = -5, and c = 3.

What is the quadratic term in the equation 7x^2 - 1/3x = 0?

The quadratic term in the equation 7x^2 - 1/3x = 0 is 7x^2.

What is the linear term in the equation 6x^2 = 9?

In the equation 6x^2 = 9, there is no linear term (no x term), so the linear term is considered to be 0.

How do you determine the constant term in the equation -8x^2 + x = 6?

To determine the constant term in the equation -8x^2 + x = 6, you need to rearrange it to the standard form -8x^2 + x - 6 = 0, where the constant term is -6.

What is the process of converting a quadratic equation into standard form?

To convert a quadratic equation into standard form, you need to rearrange the terms so that the equation is in the form ax^2 + bx + c = 0, ensuring that a is the coefficient of x^2, b is the coefficient of x, and c is the constant term.

Outlines

00:00

📚 Introduction to Quadratic Equations

This paragraph introduces the concept of quadratic equations, explaining that they are mathematical expressions involving a variable raised to the second power. The standard form of a quadratic equation is ax squared plus BX plus C equals zero, where a, b, and c are real numbers and a is not equal to zero. The speaker emphasizes the importance of identifying the values of a, b, and c in any given quadratic equation. An example is provided where the equation x squared minus 5x plus 3 equals 0 is dissected to show that a equals 1, b equals negative 5, and c equals 3.

05:03

🔍 Identifying Coefficients in Quadratic Equations

The speaker continues by discussing how to identify the coefficients a, b, and c in various quadratic equations. Examples are given to illustrate the process, such as transforming 9R squared minus 25 into a standard form where a equals 9, b equals 0, and c equals negative 25. Other examples include equations like 7x squared equals 1/3 X, which is rearranged to show a equals 7, b equals negative 1/3, and c equals 0. The importance of rearranging equations into standard form to clearly identify these coefficients is highlighted.

10:06

📘 Writing Quadratic Equations in Standard Form

This paragraph focuses on the process of writing quadratic equations in their standard form, ax squared plus BX plus C equals zero. The speaker provides several examples, such as x squared plus x equals four, which is rearranged to show a equals 1, b equals 1, and c equals negative 4. Other examples demonstrate how to handle equations without a linear term or with a constant term only. The emphasis is on correctly identifying the quadratic, linear, and constant terms and ensuring the equation is in the correct form.

15:07

🔢 Understanding the Role of Coefficients in Quadratic Equations

The final paragraph delves into the roles of the coefficients a, b, and c in quadratic equations. The speaker clarifies that even if a or c equals zero, the equation remains quadratic as long as the variable is raised to the second power. Examples are used to illustrate how the equation changes when certain coefficients are zero, such as 3x squared minus X plus 5 equals 0, which shows a equals 3, b equals negative 1, and c equals 5. The speaker concludes by reminding viewers of the importance of the second-degree exponent in defining a quadratic equation.

Keywords

💡Quadratic Equation

A quadratic equation is a polynomial equation of the second degree, typically in the form of ax^2 + bx + c = 0, where a, b, and c are constants, and x represents an unknown variable. In the context of the video, the quadratic equation is the central theme, with the script focusing on identifying and manipulating these equations into standard form and explaining their components.

💡Standard Form

Standard form in the context of quadratic equations refers to the arrangement of the equation in the format ax^2 + bx + c = 0, where the terms are ordered from the highest degree to the constant term. The video emphasizes the importance of writing quadratic equations in standard form to easily identify the coefficients a, b, and c.

💡Coefficient

In mathematics, a coefficient is a numerical factor multiplied by a variable. In the video, the coefficients a, b, and c are the numerical factors in front of the x^2, x, and the constant term, respectively. The script explains how to identify these coefficients from given quadratic equations.

💡Quadratic Term

The quadratic term in a quadratic equation is the term with the variable raised to the second power, which is ax^2 in the standard form. The video script uses the term to describe the part of the equation that contributes to its parabolic shape when graphed.

💡Linear Term

The linear term in a quadratic equation is the term with the variable to the first power, represented as bx in the standard form ax^2 + bx + c = 0. The script explains that this term affects the slope of the end parts of the parabola when the quadratic equation is graphed.

💡Constant Term

The constant term in a quadratic equation is the term without a variable, represented as c in the standard form. It is the y-intercept of the parabola when the equation is graphed and is discussed in the video as an essential part of identifying and writing quadratic equations.

💡Example

Examples in the script are used to illustrate how to identify and manipulate quadratic equations into standard form. Each example demonstrates the process of determining the coefficients a, b, and c, and ensuring the equation is correctly set to zero.

💡Graph

Although not explicitly mentioned in the transcript, the concept of graphing is implied when discussing the parabolic shape of quadratic equations. The video likely aims to help viewers understand how the values of a, b, and c affect the graph of the equation.

💡Variable

In the context of the video, the variable is the unknown quantity represented by x in the quadratic equation. The script discusses how the variable interacts with the coefficients to form the equation and how its value can be solved for.

💡Degree

The degree of a polynomial, including a quadratic equation, refers to the highest power of the variable. In the video, the term is used to distinguish between linear (first degree) and quadratic (second degree) equations, emphasizing the importance of the second degree in defining a quadratic equation.

💡Solving

While the script does not delve into solving the equations, the process of identifying coefficients and arranging the equation into standard form is a preliminary step towards solving for the variable x. The video sets the stage for understanding how to approach finding the values of x that satisfy the equation.

Highlights

Introduction to quadratic equations and their standard form.

Explanation of how to identify the coefficients a, b, and c in a quadratic equation.

Clarification that a quadratic equation must have a second-degree term.

Example of identifying a, b, and c in the equation x squared minus 5x plus 3 equals 0.

Demonstration of rearranging equations into standard form with examples.

Explanation of how to handle equations without a linear term, such as 9R squared minus 25.

Illustration of converting equations like x squared plus x equals four into standard form.

Example of rearranging 7x squared equals 1/3X into standard form.

Discussion on the importance of a being a positive real number in the standard form.

Example of converting negative eight x squared plus X equals six into standard form.

Explanation of how to handle equations with multiple terms, such as 2x plus (x minus 1) equals 6.

Clarification on the necessity of a quadratic equation to have a second-degree exponent.

Example of identifying a, b, and c in the equation 3x squared minus X plus 5 equals 0.

Discussion on the implications of a, b, or c being zero in a quadratic equation.

Final summary and encouragement to like, subscribe, and watch more videos.

Transcripts

[Music]

Hyman Akiyama in this video entitled hi

Nathan

Inaba and quadratic equation by an open

18 since auditing a quadratic equation

into standard form ax squared plus BX

plus C equals 0

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given an quadratic equation so HoloNet

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equations so Ungava Natan let's try to

identify the linear equations

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all right so Marinol on Tom Lehman

nananana Tutera Aetna lipid Sibylla ante

natal nothing linear equation now I know

burrito manga nitiram mathematical

equations so a to animate or ante natal

igniting quadratic equation pandoba not

in Malayalam and quadratic equation a

quadratic equation in one variable is a

mathematical sentence of the grid two

packs in a beam adding degree to second

degree dogmatic eaten attend so packing

dean athenian ajita eve exhibition bagua

Zhang to R squared or exponent nough to

ibig sabihin that is only a linear

equation

now since marin tae-young 2 which is on

the second degree then we can now

consider this as quadratic equation now

always remember that a quadratic

equation can be written

wedyn attention is so let into standard

form a new knob on standard form we have

a x squared plus BX plus C equals zero

where a B and C are real numbers and a

should not be equal to zero but and an

attendee not in a dapat indicia mug

equals zero or else

McGee linear equation lemon Ito no in

standard form it should be a positive

real number that and an opinion all

right let's have the parts of quadratic

equation what is a x squared this is our

quadratic term so we have three terms in

quadratic equation now what is what do

we call this

confirm bx is the linear term while c is

our constant term so in quadratic

equation in standard form ax squared is

the quadratic term BX is the linear term

and C is your constant term equals zero

okay so let's have an example let's try

to identify a B and C given the

following quadratic equation so I have

here x squared minus 5x plus 3 is equal

to 0 now I knew naba an a value B value

and C value of the given quadratic

equation so a is equal to 1 since we all

know that variable is only a little the

numerical coefficient of the variable is

always 1 next me is equal to negative 5

so after you NASA get nap and then C is

equal to 3 so Yan Lang para and PACU

Hannam e B and C you have to arrange it

first into standard form

parama who cannot enum value non a B and

C next for M squared plus 4 M plus 1 is

equal to 0 e is equal to 4 B is equal to

4 C is equal to 1 next in this give it

give an example 9 R squared minus 25 we

do not have the B value so what will be

the B value papa velasca doing some

idiotic equation so our a will be 9 me

will become 0

and then C is equal to negative 25 next

a is equal to 1/2 B is equal to 3

[Music]

okay didn't a man so last example

nothing Puma Poppins in your wallet and

constant term so therefore our C will be

zero

next how are we going to write a

quadratic equation into standard form so

remember our standard form must be

written in a x squared plus BX plus C

equals zero okay given the example x

squared plus x equals four so a lilypad

not in C for for us to have the value of

C and equated to 0 so we will have now x

squared plus X

aleady but not in C for so that will

become negative 4 is equal to 0 so we

can now get the value of a B and C is

equal to 1 B is equal to 1 C is equal to

negative 4 another example I have here 7

x squared is equal to 1/3 X so again let

us write this quadratic equation into

standard form so we will have 7 x

squared minus 1/3 X is equal to 0 so

even if at not in C one-third X and then

equate to 0 one-third X will become

negative so we will have now the value

of a which is 7 B is equal to negative

1/3 and C is equal to 0 since we do not

have

the value of Conda constant term

next we have here 6x squared is equal to

9 so let us arrange it into standard

form leap at 99 so Maggie

6x squared minus 9 remember NAFA pugna

really pata your non constant change the

sign Col du motto motto motto wishes are

equal symbol so therefore we will have

now is equal to 6 me is equal to 0 since

we do not have the linear term and then

C is equal to negative 9

next I have here negative eight x

squared plus X is equal to six

so first leap at 96 that will become

negative eight x squared plus X minus 6

gasps Emma giggling negativeness is six

and then equate to zero

now remember a guy anissina bacopa nina

non-standard form your age should be a

positive real number so since um a

methine veto a negative where the motion

a multiplied by negative one or whether

in among a divide moshe by negative one

so I'm Manya real and meet or mug to

change long tire lahat non-science

so you negative eight more Maggie Ginn

positive 8x squared young positive x

Maggie minus X u minus six Maggie Dean

plus 6 and then equals to 0 so we will

now have the value of a which is 8 B is

equal to negative 1 and C is equal to 6

neck's so it oh haha

young example so let's have an twist so

I have here say X multiplied by the

quantity of X minus 2 is equal to 10 so

we will have 3 x squared minus 1 again

sorry x squared multiplying I can say 3

x times X so when we are multiplying the

variable we are adding its exponent so

since Marron time X and the bias at Sal

all McGuigan to nasha so squared so 3

times 1 that is 3 X and X that is x

squared

next sign dominating minus 6 X 3 times

negative 2 that is negative 6 and since

we only have X 1 X or you will just copy

X and then bring down equals 10 mix a

lilypad Manhattan c10 can see that is

our constant term for us to write the

given quadratic equation into a standard

form so we will now have 3x squared

minus 6x minus 10 remember it should be

negative is equal to 0 so we can now get

a is equal to 3 B is equal to negative 6

and C is equal to negative 10

next I have here the quantity of 2x plus

5 and X minus 1 so Marin time the LaJuan

by a binomial so panin at insa is a soul

so first multiply 2x and X so that will

become 2x squared

next multiply 2x and negative 1 or minus

1 that will become negative 2x and then

5 times X that is 5x and then 5 times

negative 1 that will become negative 5

equals 6 so we will now have 2x squared

plus 3x pocket casts a mere entire

negative 2 and positive 5 so McGee

positive 3x so Buffett positive 3

because 5 is bigger than at the absolute

value of 5 is bigger than the absolute

value of negative 2 and then bring down

negative 5

bring down negative 6 next so evenly but

not in C negative 6 so McGee 2x squared

plus 3x minus 5 plus 6 remember negative

share soap agni-v but not in McGee

positive 6 is equal to 0

now since Marant IM dalja want constant

term we will combine this two so McAfee

anti-human and 2x squared plus 3x plus 1

equals 0 so we will now have a is equal

to 2 B is equal to 3 and C is equal to 1

always remember that the standard form

must be a x squared plus BX plus C

equals 0

okay so boo ha nothing's a gotten it all

let's think about this

consider 3x squared minus X plus 5 is

equal to 0 what is a in the equation

so since nifer arranged nasha into

standard form Adelina natima fajita and

value non e and that is 3 if a is equal

to 0

well the equations still be quadratic no

a guy yeah - in a bhikkhu pnina

if a will become 0 then the value of it

will well i Maggie equals ax 0 so that

will become linear equation neck next

what is B in the equation so B is equal

to a negative 1 if B will if B is equal

to 0 well the equation still be

quadratic yes we can still have a and C

what is C in the equation that is 5 if C

is equal to 0 well the equation still be

quadratic yes always remember the

quadratic equation must have a second

degree exponent so hi Edna and be at

sinatun among equals a zero that is

still awkward thank you for watching

this video I hope you learned something

don't forget to Like subscribe and hit

the bell button so our Walmart channel

just keep on watching